|
gptkbp:instanceOf
|
gptkb:Lie_group
|
|
gptkbp:actsOn
|
real (n+1)-dimensional Euclidean space
|
|
gptkbp:centralTo
|
{I, -I} for n+1 even
{I} for n+1 odd
|
|
gptkbp:compact
|
true
|
|
gptkbp:connects
|
true
|
|
gptkbp:containsElement
|
(n+1)x(n+1) real orthogonal matrices with determinant 1
|
|
gptkbp:definedIn
|
real numbers
|
|
gptkbp:determinantCondition
|
determinant = 1
|
|
gptkbp:dimensions
|
(n+1)n/2
|
|
gptkbp:fullName
|
Special Orthogonal Group of degree n+1 over the real numbers
|
|
gptkbp:fundamentalGroup
|
Z/2Z for n+1 > 2
|
|
gptkbp:generation
|
rotations in coordinate planes
|
|
gptkbp:hasSubgroup
|
gptkb:SO(n,_R)
O(n+1, R)
SO(2, R)
SO(3, R)
SO(k, R) for k < n+1
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
SO(n+1, R)
|
|
gptkbp:identityElement
|
identity matrix
|
|
gptkbp:isMaximalCompactSubgroupOf
|
gptkb:SO(n+1,_C)
SL(n+1, R)
|
|
gptkbp:isomorphicTo
|
rotation group in (n+1) dimensions
|
|
gptkbp:Lie_algebra
|
so(n+1, R)
|
|
gptkbp:notation
|
gptkb:SO(n+1,_R)
gptkb:SO(n+1)
|
|
gptkbp:order
|
infinite
|
|
gptkbp:realForm
|
gptkb:SO(n+1,_C)
|
|
gptkbp:relatedGroup
|
gptkb:group_of_people
gptkb:Lie_group
orthogonal group
simple Lie group (for n+1 > 2)
|
|
gptkbp:relatedTo
|
gptkb:Spin(n+1)
gptkb:SO(n,_R)
gptkb:rotation_group
O(n+1, R)
SU(n+1)
U(n+1)
special linear group SL(n+1, R)
|
|
gptkbp:simplyConnected
|
false
|
|
gptkbp:universalCover
|
gptkb:Spin(n+1)
|
|
gptkbp:usedIn
|
gptkb:geometry
differential geometry
group theory
physics
representation theory
|
|
gptkbp:bfsParent
|
gptkb:SO(n+1,_C)
|
|
gptkbp:bfsLayer
|
7
|